Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
446 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11719430 | C2 | semidirect |
| 2. #11719421 | C2 | semidirect |
| 3. C13×#486 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 5. #11718734 | C2 | semidirect |
| 6. #11718446 | C2 | semidirect |
| 7. #11718443 | C2 | semidirect |
| 8. #11718355 | C2 | semidirect |
| 9. C4×#6094 | C2 | semidirect |
| 96. #1055 | #41 | semidirect |
| 102. #486 | D13 | semidirect |
| 188. C13 | #3184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719430 | 2 |
| #11719421 | 2 |
| C13×#486 | 2 |
| #11718740 | 2 |
| #11718734 | 2 |
| #11718446 | 2 |
| #11718443 | 2 |
| #11718355 | 2 |
| C4×#6094 | 2 |
| #3184 | 13 |